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Simplifying 100x2 + x + -5066104.5 = 0 Reorder the terms: -5066104.5 + x + 100x2 = 0 Solving -5066104.5 + x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -50661.045 + 0.01x + x2 = 0 Move the constant term to the right: Add '50661.045' to each side of the equation. -50661.045 + 0.01x + 50661.045 + x2 = 0 + 50661.045 Reorder the terms: -50661.045 + 50661.045 + 0.01x + x2 = 0 + 50661.045 Combine like terms: -50661.045 + 50661.045 = 0.000 0.000 + 0.01x + x2 = 0 + 50661.045 0.01x + x2 = 0 + 50661.045 Combine like terms: 0 + 50661.045 = 50661.045 0.01x + x2 = 50661.045 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01x + 0.25 + x2 = 50661.045 + 0.25 Reorder the terms: 0.25 + 0.01x + x2 = 50661.045 + 0.25 Combine like terms: 50661.045 + 0.25 = 50661.295 0.25 + 0.01x + x2 = 50661.295 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 50661.295 Calculate the square root of the right side: 225.080641104 Break this problem into two subproblems by setting (x + 0.5) equal to 225.080641104 and -225.080641104.Subproblem 1
x + 0.5 = 225.080641104 Simplifying x + 0.5 = 225.080641104 Reorder the terms: 0.5 + x = 225.080641104 Solving 0.5 + x = 225.080641104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 225.080641104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 225.080641104 + -0.5 x = 225.080641104 + -0.5 Combine like terms: 225.080641104 + -0.5 = 224.580641104 x = 224.580641104 Simplifying x = 224.580641104Subproblem 2
x + 0.5 = -225.080641104 Simplifying x + 0.5 = -225.080641104 Reorder the terms: 0.5 + x = -225.080641104 Solving 0.5 + x = -225.080641104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -225.080641104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -225.080641104 + -0.5 x = -225.080641104 + -0.5 Combine like terms: -225.080641104 + -0.5 = -225.580641104 x = -225.580641104 Simplifying x = -225.580641104Solution
The solution to the problem is based on the solutions from the subproblems. x = {224.580641104, -225.580641104}
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